Short Answer
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1.
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At D. J.’s Drink Stand, Erika ordered a cup of fruit punch made with the
following recipe.  cup
lemonade  cup cranberry
juice cup orange juice What fraction of Erika’s cup will be orange
juice? Write a number sentence to support your answer.
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2.
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Mr. Gomez took some of his cross-country team out for pizza the night before a
big race. He ordered three medium pizzas. They ate the following amounts: Scott ate  of a pizza. Nate ate  of a
pizza. Da-Wei ate  of a
pizza. Mr. Gomez ate  of a
pizza. a. How many pizzas did
they eat? Write a number sentence to support your answer.
b. How many pizzas were left? Write a number sentence to support your
answer.
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3.
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For parts (a)–(d), find each sum or difference. Show all your
work.
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4.
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Bob is making treat bags for his daughter’s birthday party. He decided to
use the recipe below for each bag. He needs to make 6 bags so each friend can have one and he wants
to make  bag for his two-year-old to have as well. How much
of each ingredient will he need to make the  bags? Write number sentences to
support your answer.
Recipe for 1 Bag  cup peanuts  cup
pretzels  cup raisins  cup popcorn
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5.
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On a particular map of Denmark, 1 inch on the
map represents 12 miles.
a. What does  inches on the map
represent? Write a number sentence and show your work. b. What does  inches on the map
represent? Write a number sentence and show your work.
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6.
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Caroline had a pan of lasagna  full. She had some friends over
for lunch and the friends ate  of the pan of lasagna. a. How much of the pan of lasagna did her friends eat? Use a drawing
and a number sentence to support your answer.
b.
Savannah had a lasagna pan  full. She had friends over for lunch and they ate
 of the pan of lasagna. How is this different from what happened with Caroline’s pan
of lasagna? c. How is this the same as what happened with Caroline’s pan of
lasagna?
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7.
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Write a story problem to fit the computation below. Explain why the calculation
matches the story.
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8.
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Gregorio made money over his summer vacation by mowing lawns. One week he worked
the following schedule:
| Monday | 
hours | | Wednesday |  hours | | Thursday |  hours | | Friday |  hours | | |
a. How
many hours did Gregorio work for the week?
b. He needs to work 20 hours to earn the money for
a trip. Will he have enough after working just this one week? Explain your thinking.
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9.
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Jin-Lee and Sarah decide to make a pancake breakfast for six people. They found
a recipe that will make 12 silver-dollar pancakes per batch. They need 30 silver-dollar pancakes to
give 5 per person. How much of each ingredient will they need to make 30 silver-dollar
pancakes?
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10.
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If each person in North America throws away  pounds of garbage
each day, how many pounds of garbage does each person throw away in a year?
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Find the value of N. Show your work.
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11.
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12.
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a. Estimate
the following and explain how you made your estimate:
b. For each problem in part (a), find the exact sum or
difference.
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13.
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a. Use fraction addition to find this sum:
1.23 + 3.9 b. Use decimals and place value to find this sum: 
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14.
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Every night Dan’s dad puts any pennies or nickels he has in his pocket
into a container for Dan. Dan does not remove any money. Dave next door has the same arrangement with
his mom. Here is the data from the third week:
a. Who had the most on
Wednesday and by how much?
b. Who made the most over the week and by how much?
c.
How much would Dan and Dave have if they combined their money on Friday?
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15.
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For each pair of problems, which computation gives the larger answer? Show your
work. | a. 1.809 + 18.09 | or | 7.05 + 11.918 | | b. 27.01 – 22.503 | or | 5.021 – 0.514 | | c. 0.37 ´ 7.5 | or | 25.13
´ 0.037 | | d.
12.5 ÷ 0.25 | or | 1.1 ÷
0.02 | | | |
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16.
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Sam has to solve this computation problem: 3.05 ÷ 0.05 = ? a. Write a story problem that would require the given
division.
b. What does the 3 in the number 3.05 mean in place-value terms?
c. What does the 5 in the number 0.05 mean in place-value
terms?
d. Show how to write the problem as a fraction
problem with common denominators and then find the solution.
e. What does the solution to the division mean? (What does it tell
you?)
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17.
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Insert decimal points into the two factors, so that each of the following
problems have different factors but give the same product. Explain how you made the problems. | Problem 1 | Problem
2 |  |  | | |
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18.
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Insert decimal points into the two factors so that each of the following
problems give the correct product. Explain how you made the problems.
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19.
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Josh and his father are estimating how much gas they will need for a car trip.
They know the car got 39.2 miles per gallon on a similar trip last month. A computer printout of
directions lists the trip as 778.4 miles. Estimate how many gallons of gas they will need for the
trip. Explain you how made your estimate.
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20.
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The diagram below shows a rectangular plot of land cut into squares of 2.65
acres each. a. What is the acreage of the shaded region? Explain your
reasoning.
b. What is the acreage of the unshaded region? Explain your
reasoning.
c. In this area, land sells for $2475 per acre.
i. What would the price of the shaded region be?
ii.
What would the price of the unshaded region be?
d. In
this area, owners pay property taxes of $13.50 per thousand dollars of property value. What is the
total annual property tax for the shaded and unshaded regions combined? Explain your
reasoning.
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Use the number sentence to help you solve the following problems.
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21.
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123 ´ 4 = 492 | a. 12.3 ´ 4 | b. 1.23 ´ 4 | c. 0.123 ´ 4 | | d. 0.123 ´ 40 | e. 0.123 ´ 400 | f.
0.123 ´ 4000 | | | |
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22.
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63 ´ 501 = 31,563 | a. 6.3 ´ 5.01 | b. 6.3 ´ 0.501 | c. 6.3 ´ 50.1 | | d. 0.63 ´ 5.01 | e. 0.63 ´ 501 | f.
0.63 ´ 0.501 | | | |
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23.
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The student council at Metropolis Middle School conducted a survey to see
whether students would prefer blue, red, or green as the new color for the school logo. The results
of the survey are shown in the bar graph below. a. What is the total number of students who were surveyed? Explain
how you found your answer.
b. What percent of students
surveyed preferred blue?
c. What percent of students surveyed preferred red?
d.
What percent of students surveyed preferred green?
e.
If 970 students attend Metropolis Middle School, what percent of the students were surveyed? Explain
how you found your answer.
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24.
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Decide if each of the following statements is true or false. Explain your
reasoning. a. Any two parallelograms with the same side
lengths have the same area.
b. Any two triangles with the same side lengths have the same
area.
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25.
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The Acme sign company makes traffic signs for the state road commission. A
model of the signs and their approximate measurements are given below. a. One of the costs that Acme must consider is the cost of
metal. If metal costs $1.00 for every 1000 square centimeters, what is the cost of the metal
for each sign?
Yield sign:
School zone sign:
Speed limit
sign:
Railroad crossing sign:
b. After the signs are
cut, the edges must be sanded to prevent metal splinters. If the cost of sanding is 2 cents for
every centimeter, what will it cost to sand each sign?
Yield
sign:
School zone sign:
Speed limit sign:
Railroad
crossing sign:
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26.
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Find the area and perimeter of each shape below.
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27.
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A. 1. Find the area of each triangle below. 2. How are the heights of these
triangles related to each other?
3. How are the areas of these triangles related to each
other?
B. 1. Find the area of each triangle below. 2. How are the bases of these
triangles related to each other?
3. How are the areas
of these triangles related to each other?
C. 1. Find
the area of each triangle below.
2. Based on the patterns in parts A
and B, sketch the third triangle.
3. How are the heights of these triangles related to each
other?
4. How are the bases of these triangles related to each other?
5. How are the areas of these triangles related to each
other?
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28.
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Use the diagram below to answer the following questions. a. If the perimeter of the
parallelogram is 14.4 centimeters, what is the length of the base? Explain your
reasoning.
b. What is the area of the parallelogram? Explain your reasoning.
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29.
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Consider each distribution below. For each distribution, where possible, tell
how many people are represented by the data, and identify the mode, median, and range. a.
b.
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30.
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Make a line plot showing the lengths of 11 names so that the median length is 12
letters and the range is from 6 letters to 16 letters.
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31.
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The media specialist in your school is planning a book fair. She is preparing a
survey to ask students a few questions to help make the book fair a success. a. Write one question that will give the media specialist
numerical data. Explain why she might want to know this information.
b. Write one question that will give the media specialist
categorical data. Explain why she might want to know this information.
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32.
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Fifteen students read the book Gulliver’s Travels. In the book, the
Lilliputians said they could make clothes for Gulliver by taking one measurement, the length around
his thumb. The Lilliputians claimed that • the distance
around Gulliver’s wrist would be twice the distance around his thumb.
• the distance
around Gulliver’s neck would be twice the distance around his wrist.
• the distance
around Gulliver’s waist would be twice the distance around his neck.
The students
wondered whether this doubling relationship would be true for them, too. They measured the distance
around their thumbs and their wrists in centimeters, then graphed the pairs of numbers on a
coordinate graph. They drew a line connecting the points that represented wrist measurements that
were twice thumb measurements.
a. How many students’ measurements fit the Lilliputian rule
that twice the distance around the thumb equals the distance around the wrist?
b. How many
students’ wrist measurements are less than twice their thumb measurements?
c. The
point for Jeri’s thumb and wrist measurements is above the line. If the cuffs of a shirt are
twice the measurement around Jeri’s thumb, how will the cuffs of the shirt fit
her?
d. The point for Rubin’s thumb and wrist measurements is below the line. If the
cuffs of a shirt are twice the measurement around Rubin’s thumb, how will the cuffs of the
shirt fit him?
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33.
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A group of students were curious about the changes in people’s height over
time. They gathered data about height from two different groups of students in their district:
students in grade 5 and students in grade 8. The data they collected is shown in the table.
a.
Organize and display these data using an appropriate graph or plot.
b. What is the typical
height of a grade 5 student? Justify your answer.
c. What is the typical height of a grade
8 student? Justify your answer.
d. How does the distribution of height data from the grade
5 class compare with the distribution of height data of the grade 8 class?
e. There were
three grade 8 students absent the day the data were collected. Their heights are 177 cm, 187 cm, and
163 cm. What happens to the mode and median when these new pieces of data are added to the data
set?
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34.
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For the distribution below, tell how many people are represented and identify
the mode, median, and range.
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35.
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Make a line plot showing the ages in years of 12 students so that the median age
is 12.5 years and the difference between the highest age and the lowest age is 9 years.
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36.
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The mean number of children in six families is 5 children. a. What is the total number of children in the six families?
b.
Other than six families of 5 children, create a set of families that fits this
information.
c. Would another classmate’s set of families for question (b) have to be
the same as yours? Explain.
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37.
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In the story The Phantom Tollbooth, Milo is told that the average number
of children in a family is 2.58. You know that a 0.58 boy or girl cannot exist. How can the
calculations for the mean produce a number representing a child that does not seem to make
sense?
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38.
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Most people will walk about 158,125 kilometers in their lifetime, or around the
world 4.5 times. a. How do you suppose this statistic was
determined?
b. What might you do if you were asked to investigate the question, “How
far do most people walk in their lifetime?”
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39.
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A class investigated how many pets each student in the class had. A number of
students in their class had no pets at all. Here’s how their data looked:
a. Would it be possible to have a data set for which the median
number of pets for students is 0? Explain.
b. Would it be possible to have a data set for
which the mean number of pets for students is 0? Explain
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40.
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Ms. Snow had her students write down a whole number between 1 and 10 on a slip
of paper. Then she collected the numbers and displayed the data in a line plot. Use the line plot to
answer the following questions. a. What is the typical number chosen by students in this class?
b. If two students were absent on the day Ms. Snow
collected the data, how many students are enrolled in the class? Explain your reasoning.
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41.
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Mr. Watkins arranged the quiz scores of his afternoon math class from least to
greatest: 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9,
10, 10
a. How many students are in Mr. Watkins’s
afternoon math class? Explain how you found your answer.
b. How do the range of the
quiz scores vary? c. What is the mode of the scores? d. What is the median of the
scores?
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42.
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The students in Mr. Furgione’s math class counted the letters in the names
of the streets where they lived. Then they made the bar graph below. Use the bar graph to answer the
following questions.
a. Make a table showing each name length and the number of students
who live on streets with names of that length. Then make a line plot showing these name
lengths.
b. Nobody was absent when the data were collected. How many students are in Mr.
Furgione’s class? Explain how you found your answer.
c. What is the typical street-name length for this class? Use the
mode, median, and range to help you answer this question.
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Make a line plot or a bar graph of a set of name-length data that fits the
description.
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43.
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24 names that vary from 6 letters to 18 letters
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44.
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The members of the drama club sold candy bars to help raise money for the
school’s next play. The stem-and-leaf plot below shows how many candy bars each member of the
drama club sold. a. How many students are in the drama club? Explain how you found
your answer.
b. How many students sold 25 or more candy bars? c. How do the
numbers of candy bars sold by each student vary? d. What is
the typical number of candy bars sold by each student?
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45.
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Taryn and Travis work in the student store at their school. They made the
coordinate graph below to show the total sales each day for three weeks. There are three points
corresponding to each weekday because Taryn and Travis recorded their data for the three weeks on a
one-week graph. a. What were the total sales on
Tuesdays for the three weeks Taryn and Travis collected their data?
b. Which day of the week seems to be the best for sales at the
student store? Explain your reasoning.
c. Which day of the week varies the most for total
sales? Explain your reasoning.
d. How do the sales for the entire three-week period vary?
Explain your reasoning.
e. What is the median of the total sales for Fridays? What is the
median of the total sales for the three weeks Taryn and Travis collected data? Explain how you found
your answers.
f. Describe the pattern of sales during a
typical week at the student store.
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46.
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Emily rolled two four-sided number cubes 12 times and computed the sum for each
roll. She recorded the results as ordered pairs. The first coordinate is the number of the roll, and
the second coordinate is the sum for that roll. For example, (9, 2) means that on her ninth roll
Emily rolled a sum of two. The results of Emily’s rolls were: (1, 7), (2, 8), (3, 3), (4, 4),
(5, 6), (6, 3), (7, 5), (8, 6), (9, 2), (10, 4), (11, 5), (12, 5). a. Make a coordinate graph of Emily’s data. Use the horizontal
axis for the number of the roll and the vertical axis for the result.
b. What is the mode of the sums of Emily’s rolls?
Explain.
c. What is the range of the sums?
d. What is the median of the sums?
Explain.
e. Does the coordinate graph you made in part
a show a pattern in Emily’s number-cube rolls? Explain.
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47.
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The mean amount of change that Betty, Bill, and Susan have in their pockets is
79 cents. What is the total value of the change they have together? Explain how you found your
answer.
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48.
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Glenda rolled two six-sided number cubes nine times and computed the sum of the
numbers rolled each time. a. If the mean sum of
Glenda’s rolls was 6, what was the total of the nine sums Glenda rolled?
b. Suppose
Glenda’s rolls were 12, 7, 3, 10, 9, 2, 11, 7, and 8.
i.
What is the median of Glenda rolls?
ii. What is the mean of Glenda’s rolls?
iii. What is
the mode of Glenda’s rolls?
iv. Which do you think is
the best indicator of a typical roll Glenda made, the median, mean, or mode? Explain your
reasoning.
c. Suppose Glenda rolled a total sum of 60
for her nine rolls.
i. What is the mean sum for the rolls
Glenda made?
ii. Give an example of nine rolls that Glenda
could have made. Explain how you found your answer.
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49.
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The stem plot below shows test scores for Ms. McIntyre’s class on a state
mathematics test. Students can score from 0 to 100 points. a. What is the range of the
data?
b. What is the median of the data? How many students had a score the same as the
median?
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50.
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Rachel has tossed a fair coin ten times, and it has landed heads up every time.
a. Is this possible? Explain.
b. Is this likely?
Explain.
c. Which of the following statements is true about what will happen when Rachel
tosses the coin again? Why?
i. The coin will land heads
up.
ii. The coin will land tails up.
iii. The chances of
the coin landing heads up or tails up are equal.
iv. The coin is more likely to land heads up.
v. The coin is more likely
to land tails up.
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51.
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The probability of a particular event is  . What is the
probability that the event will not happen? Explain.
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52.
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Give an example of a situation with outcomes, which are not equally
likely.
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53.
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Which of the following numbers could not be the probability of an event?
Explain.
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54.
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Mandy has a bag containing one green block (G), one brown block (B), and one
yellow block (Y). She conducted 20 trials in which she drew one block from the bag and then flipped a
fair coin. Here are the results of her experiment: G-T, Y-T,
G-H, G-T, Y-H, Y-T, B-T, Y-H, G-T, Y-T,
B-T, Y-H, B-T, Y-T, Y-T, B-T, G-H, G-T, Y-H,
Y-T
a. What is
the experimental probability of drawing the brown block and flipping heads? What is the theoretical
probability?
b. What is the experimental probability of drawing the yellow block and
flipping tails? What is the theoretical probability?
c. How would you explain the
differences you found between the experimental and theoretical probabilities?
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55.
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Two radio stations are playing the #1 hit song “2 Nice 2 B True” by
Anita and the Goody-2-Shoes. WMTH plays the song every 18 minutes. WMSU plays the song every 24
minutes. Both stations play the song at 3:00 P.M. When is the next time the stations will play the
song at the same time?
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56.
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Judith is planning a party for her younger brother. She has 36 prizes and 24
balloons. How many children can she have at the party so that each child gets an equal number of
prizes and an equal number of balloons? Explain your answer.
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57.
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Find three different ways to show factorizations (strings of factors) of the
number 16. Do not use 1 as a factor.
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58.
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Find the prime factorization of the following two numbers. Show your
work.
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59.
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A number that is less than 85 has 26 and 6 as factors. Find the number and
explain your reasoning.
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60.
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What number has the prime factorization  ? Show how you
found the number.
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61.
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“Sam” and “Martha” are the local names for two
lighthouses that guard a particularly dangerous part of the coast. Sam blinks every 12 seconds and
Martha blinks every 8 seconds. They blink together at midnight. How many seconds will pass before
they blink together again?
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62.
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Carlos is packing sacks for treats at Halloween. Each sack has to have exactly
the same stuff in it or the neighborhood kids complain. He has on hand 96 small candy bars and 64
small popcorn balls.
a. What is the greatest number of treat sacks he can
make?
b. How many of each kind of treat is in one sack?
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63.
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a. What is the greatest common factor of 30 and 42?
b. Give
a different common factor of 30 and 42.
c. What is the least common multiple of 30 and
42?
d. Give an additional common multiple of 30 and 42.
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64.
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Dawson wrote the factorization  . Without finding the actual
number, how can Dawson tell if the number is even or odd?
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65.
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a. Use an angle ruler to draw a 100°
angle.
b. Use an angle ruler to measure the following
angle. 
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66.
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One of the most common places we see angles is on the faces of clocks. At the
start of each hour, the minute hand is pointed straight up, at the 12. Without using an angle ruler, find the measure of the following
angle.
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Decide whether the given statement is true or false. Give explanations or
sketches to support your answers.
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67.
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All rectangles are special kinds of parallelograms.
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68.
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All parallelograms are special kinds of squares.
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69.
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G. Oni O’Meter is a math rap singer who lives in Miami, Florida. She is
starting a fall concert tour, and she flies her own plane to every concert. Here is her tour
schedule: To fly from one
city to the next, G. Oni needs a flight angle and compass direction to direct her plane. A flight
angle is formed by two lines that start in the city from which the flight takes off. One line points
north, and the other points to the flight’s destination. The flight angles are labeled with
degree measure and west or east.
For example, to fly from
Miami to Dallas for the first concert, G. Oni flies along a 71° west flight angle. Using your
angle ruler and the map below, find the flight angles for the rest of G. Oni’s concert
tour. 
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70.
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In the diagram, line L1 is parallel to line
L2.
a. What is the measure of Ð 3?
Explain how you found your answer.
b. What is the measure of Ð
1? Explain how you found your answer.
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Use an angle ruler to measure each angle.
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71.
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72.
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Use these shapes for the following question.
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73.
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The figures I, L, and V can be grouped together, but X would not belong in the
group. Explain.
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74.
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The figures E, G, H, I, and M can be grouped together, but S would not belong in
the group. Explain.
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75.
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The figures F, Q, W, and X can be grouped together, but N would not belong in
the group. Explain.
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76.
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Use the quadrilateral shown below to answer parts (a)–(b).  a. Find the measures of angles 1, 2, 3, and
4. Explain your answers.
b. Are any of the sides of the quadrilateral
parallel?
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Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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77.
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Find the product.
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78.
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 ´ 
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Use mental math to find the product.
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79.
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80.
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100(6.3)
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81.
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Theo made the table below to show the number of middle school students who
attended the last football game. If this data were displayed in a circle graph, what percent of the
graph would represent the eighth graders who attended the game?
Grade
| Number of Students in Attendance | 6 | 375 | 7 | 275 | 8 | 350 | | |
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82.
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A survey about the student government program at a school finds the following
results:
110 students like the program, 120 students think the program is unnecessary, and 210
students plan on running for student government next year. If a circle graph were made from this
data, what would the measure of the central angle be for the think the program is unnecessary
group?
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83.
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Find the measure of the central angle that you would need to draw to represent
86% in a circle graph. Round to the nearest degree if necessary.
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84.
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Five students competed in a free throw contest. The number of free-throws out of
10 each student made is charted below. Based on the chart below, which of the following statements is
false? a. | Amy made more free throws than Shea or Jill | b. | Mark made more free
throws than Jill | c. | Nate made the most free throws | d. | Shea made less free throws than Nate and
Amy |
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85.
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Students in 7th grade history classes are selling magazines to go on
class trips. There are 6 different history class periods that are selling magazines. The graph below
shows the number of magazines sold by students in the different class periods. How many more
magazines were sold by class period 2 than class period 4?
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86.
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The stem-and-leaf plot shows the number of cans of food collected by various
students for a food drive. How many students collected more than 43 cans? Stem | Leaves | 3 | 0 1 1 1 4 4
4 | 4 | 0 1 3 4 4 5 | 5 | 0 3 3 6 8 | | |
key: 3 | 5 means
35
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87.
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The stem-and-leaf plot shows the number of fish that were caught by several
ships in a fishing fleet. How many ships caught 37 fish or fewer? | Stem | Leaves | | 3 | 0 3 3 5 6 | | 4 | 0 2 4 5 8 9 9 | | 5 | 0 1 2 4 | | |
key: 2 | 4 means 24
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88.
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Which of these drawings shows AB parallel to CD and CD
perpendicular to EF?  a. | Figure A | b. | Figure B | c. | Figure C | d. | Figure
D |
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89.
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In the diagram, p || q. Find the measure of each numbered
angle.  a. | mÐ1 = mÐ2 = mÐ5 = 50º
mÐ3 = mÐ4 = mÐ6 = mÐ7 = 130º | c. | mÐ1 = mÐ2 = mÐ5 = 120º
mÐ3 =
mÐ4 = mÐ6 =
mÐ7 = 50º | b. | mÐ1 =
mÐ2 = mÐ5 =
130º
mÐ3 = mÐ4
= mÐ6 = mÐ7
=50º | d. | mÐ1 = mÐ2 = mÐ5 = 130º
mÐ3 =
mÐ4 = mÐ6 =
mÐ7 = 45º |
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90.
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If a and b are parallel lines and mÐ4 = 45º, what is the measure of Ð7? 
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